Trigonometry Introduction Practice Tests

These Grade 10 Geometry practice tests introduce right-triangle trigonometry through sine, cosine, tangent, special angles, missing sides, and practical measurement problems.

Skills covered

  • Identifying the hypotenuse, opposite side, and adjacent leg relative to an acute angle
  • Using SOHCAHTOA to calculate sine, cosine, and tangent ratios
  • Finding missing sides with trigonometric ratios and the Pythagorean Theorem
  • Using 30°, 45°, and 60° special-angle values and complementary-angle relationships
  • Applying trigonometry to ladders, ramps, shadows, buildings, towers, roofs, cables, and elevation problems

How to use these practice tests

Start by labeling the reference angle and the three sides of the right triangle. Choose sine, cosine, or tangent based on the sides involved, then check whether the answer has a reasonable length and unit.

For more Grade 10 Math practice, return to the Grade 10 Math category.

4. Test

Grade 10 Trigonometry Introduction Practice Tests

Practice Grade 10 Geometry questions about right triangles, sine, cosine, tangent, SOHCAHTOA, special angles, inverse reasoning, and real-world applications.

Choose the best answer. Identify the reference angle and the opposite, adjacent, and hypotenuse sides before selecting a ratio or special-angle relationship.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is sin⁡30°\sin30°?

Please select an answer first.

Correct answer: A

The correct answer is 12\frac{1}{2}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: The 30°-60°-90° triangle gives sin⁡30°=1/2\sin30°=1/2.
  3. Check the result: The correct answer is 12\frac{1}{2}..

The 30°-60°-90° triangle gives sin⁡30°=1/2\sin30°=1/2.

2. QuestionMultiple choice

What is cos⁡60°\cos60°?

Please select an answer first.

Correct answer: B

The correct answer is 12\frac{1}{2}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: The 30°-60°-90° triangle gives cos⁡60°=1/2\cos60°=1/2.
  3. Check the result: The correct answer is 12\frac{1}{2}..

The 30°-60°-90° triangle gives cos⁡60°=1/2\cos60°=1/2.

3. QuestionMultiple choice

What is tan⁡45°\tan45°?

Please select an answer first.

Correct answer: C

The correct answer is 1..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: A 45°-45°-90° triangle has equal legs, so opposite over adjacent equals 1.
  3. Check the result: The correct answer is 1..

A 45°-45°-90° triangle has equal legs, so opposite over adjacent equals 1.

4. QuestionMultiple choice

What is sin⁡45°\sin45°?

Please select an answer first.

Correct answer: D

The correct answer is 22\frac{\sqrt{2}}{2}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: In a 45°-45°-90° triangle, each leg-to-hypotenuse ratio is 2/2\sqrt{2}/2.
  3. Check the result: The correct answer is 22\frac{\sqrt{2}}{2}..

In a 45°-45°-90° triangle, each leg-to-hypotenuse ratio is 2/2\sqrt{2}/2.

5. QuestionMultiple choice

What is cos⁡30°\cos30°?

Please select an answer first.

Correct answer: A

The correct answer is 32\frac{\sqrt{3}}{2}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: The 30°-60°-90° triangle gives cos⁡30°=3/2\cos30°=\sqrt{3}/2.
  3. Check the result: The correct answer is 32\frac{\sqrt{3}}{2}..

The 30°-60°-90° triangle gives cos⁡30°=3/2\cos30°=\sqrt{3}/2.

6. QuestionMultiple choice

What is tan⁡60°\tan60°?

Please select an answer first.

Correct answer: B

The correct answer is 3\sqrt{3}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: The 30°-60°-90° triangle gives tan⁡60°=3\tan60°=\sqrt{3}.
  3. Check the result: The correct answer is 3\sqrt{3}..

The 30°-60°-90° triangle gives tan⁡60°=3\tan60°=\sqrt{3}.

7. QuestionMultiple choice

An acute angle has sine 12\frac{1}{2}. What is the angle?

Please select an answer first.

Correct answer: C

The correct answer is 30°..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: Among the common acute special angles, sin⁡30°=1/2\sin30°=1/2.
  3. Check the result: The correct answer is 30°..

Among the common acute special angles, sin⁡30°=1/2\sin30°=1/2.

8. QuestionMultiple choice

An acute angle has cosine approximately 0.707. What is the angle?

Please select an answer first.

Correct answer: D

The correct answer is 45°..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: The special-angle value cos⁡45°=2/2≈0.707\cos45°=\sqrt{2}/2\approx0.707.
  3. Check the result: The correct answer is 45°..

The special-angle value cos⁡45°=2/2≈0.707\cos45°=\sqrt{2}/2\approx0.707.

9. QuestionMultiple choice

An acute angle has tangent 3\sqrt{3}. What is the angle?

Please select an answer first.

Correct answer: A

The correct answer is 60°..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: The special-angle value tan⁡60°=3\tan60°=\sqrt{3}.
  3. Check the result: The correct answer is 60°..

The special-angle value tan⁡60°=3\tan60°=\sqrt{3}.

10. QuestionMultiple choice

If one acute angle in a right triangle is 38°, what is the other acute angle?

Please select an answer first.

Correct answer: B

The correct answer is 52°..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: The two acute angles are complementary, so the other is 90°−38°=52°90°-38°=52°.
  3. Check the result: The correct answer is 52°..

The two acute angles are complementary, so the other is 90°−38°=52°90°-38°=52°.